There are many dependent variables that no matter how many transformations you try, you cannot get to be normally distributed. The most common culprits are count variables–the variable that measures the count or rate of some event in a sample. Some examples I’ve seen from a variety of disciplines are:
Number of eggs in a clutch that hatch
Number of domestic violence incidents in a month
Number of times juveniles needed to be restrained during tenure at a correctional facility
Number of infected plants per transect
A common quality of these variables is that 0 is the mode–the most common value. 1 is the next most common, 2 the next, and so on. In variables with low expected counts (number of cars in a household, number of degrees earned), (more…)